Counting

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It is the simplest natural materials that seem to inspire the most play.

This is often the case in my classroom. When I put open-ended natural materials in the math area children find many mathematical ways to use them.

As I watched children playing with rocks and ten-frames inside, I had the idea to bring these materials (back) outside.

For this playful invitation, think about games you can play using large ten frames.

How to Use the Blog Posts

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PLAYFUL INVITATION 

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1.    Prepare: Gather chalk and a large dice. The one we used was created using an old tissue box. Then, draw a large ten frame with chalk.

Use the Invitation to Play Documentation Tool to collect data. 

2.    Invite: Would you like to play a game? Roll the dice and whatever number you roll find that many things.

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3.    Play: The first round you might model how to play. Roll the dice and call out the number rolled.

Explain that you are going to find the same number of things around the playground/yard. Quickly run and find the same amount rolled then bring them back to the ten frame. Use one-to-one correspondence, placing one item in each box.
Count how many you found and match it to the dice.

Once you complete the first roll, either roll again, or ask the child to count how many more they need to fill the whole ten-frame. Challenge the child to find that many more.

*When my class played we set a timer for 30-60 seconds and tried to find our natural materials before the timer went off. Also, for a few rounds we choose a material and called out to only find leaves, flowers, sticks, etc.

4.    Reflect and Assess: Did children quickly call out the number rolled (subitize) or did they count each pip on the dice? Did children match quantity on the dice with the number of items they found? Were children able to fill the ten frame by counting the remaining empty squares.

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Measurement

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Last summer we visited a Llama farm in rural Minnesota. My children had the opportunity to be up close and personal with these gentle creatures. As my two year old ran around the farm, she zeroed in on a baby Llama, hugging and petting it’s head and neck, exclaiming “you’re so tiny” and “you’re so little.” Eventhough, the baby Llama was bigger than my daughter (so not exactly tiny), by comparison to the mama, this one was small.  Seeing the baby next to its mother gave her perspective to determine a difference in size.

But what if you can’t compare objects directly? What if you want a more precise comparison? Sometimes you need to use a unit to measure and then compare. Our invitation today is to practice measuring using nonstandard units determined by an item you find outside.  (ex. It is two leaves long, It is five pinecones wide)

To compare objects, children begin by using nonstandard units (“My table is more than four hands long”) and then move to using standard units (“The table is almost three feet long”). Comparing fairly is an important concept for young children. - Juanita Copley, 2010

How to Use the Blog Posts

PLAYFUL INVITATION

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1. Prepare: Gather chalk and natural materials that are consistent in size. For example, leaves from one tree, pinecones, sticks, etc.

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.

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2.    Invite: Today I thought we could trace our bodies so we can see how big we are. (After tracing one or more bodies) I wonder whose body is the tallest/longest?

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3.    Play: Have each child lay on the ground and draw a chalk outline of his/her body. After the bodies are drawn provide a giant basket of one type of object. Be sure they are all similar size.

Model: Look how I lay these side by side from the top of your body to the bottom. Now let’s count how many we used…. Count together and write the number.

Look at the next body outline and do the same thing. Compare.  Which was the longest?

Explain: We can measure using all kinds of different things. Next time let’s measure using sticks.

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4.    Reflect and Assess: What did you observe about the child’s knowledge of measurement.

Ready: This playful invitation would be best suited for older preschool or kindergarten children who can count with understanding, use the language of comparison and measurement to talk about size (same, different, bigger, smaller, long, tall), and have experience comparing objects.

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Extend: Begin to introduce measuring tapes or rulers into the writing center and dramatic play. Continue to focus on nonstandard units for measuring until the children seems ready to advance.

Also, try filling the outline of the body with one material, and talk about area.  How many leaves did you need to fill the entire body. Count, compare.

RESOURCES

Copley, J.V. (2010). The young child and mathematics (2nd. ed.). Washington, D.C: National Association for the Education of Young Children and National Council of Teachers of Mathematics.

Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson Education.

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Math Talk

Every page asks the same question, and every answer can be correct.

-Christopher Danielson

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I recently had the good fortune of pulling two Christopher Danielson books off the shelf at my local library. I have to admit I didn’t realize the books were by the same author until we were nestled into our reading chair and well into the second book.

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These clever texts are a treasure trove for math enthusiasts: parents, teachers and others. If you haven’t seen them then I strongly urge you to pick them up from a library or bookstore.

How Many?

Each page shows a real image of one or more things, then asks the reader “How many?”

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Now the fun part. Danielson guides the reader, saying that the book won’t tell you what to count, instead you decide. For example, the egg carton with one egg might naturally lead you to say “1 egg,” but another viewer may count “12 cups in the egg carton,” or “4 holes in the top.”

What makes this open-ended adventure in counting even more fun is when you read with another person and talk about what they counted and why.

So many possibilities for open-ended questions, conversation and counting!

Which One Doesn’t Belong?

Each page shows four shapes and asks, “Which one doesn’t belong?” The question encourages the reader to think deeply. There is no “right” answer. The real question is then “Why?” Explain your thinking.

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Conversation comes naturally as you move through the book. I was blown away by the unique and surprising answers my own children gave as we explored the pages.

Not only that, by reading the book together and sharing our ideas we were developing those great 21st century skills of communication, collaboration, critical thinking and creativity.

These books are so much fun. I know we will read them again and again.

Check out more from Dr. Christopher Danielson

https://talkingmathwithkids.com

Visit him at the Minnesota State Fair

https://www.mnstatefair.org/location/math-on-a-stick/

Spatial Relationships

Whenever I do puzzles with my three year old I have to stop myself from providing too much help. Sometimes I worry that she’ll get frustrated if it’s too hard, or I’ll get impatient and want to speed things up. I hand her pieces that are right-side up and positioned for easy placement. I need to slow down. I’m trying to remind myself to take a step back, observe, and allow her the chance to work out all the transformations needed to find the perfect fit.  As a boy in a kindergarten class I was observing said to his classmate, “Don’t steal her struggle!”

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How to Use the Blog Posts

PLAYFUL INVITATION

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1.    Prepare:  Find a variety of leaves and a pair of scissors. Cut a few leaves in half.

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.

2.    Invite: I’m trying to put this leaf back together! Will you help me find the perfect match to make my leaf complete?

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3.    Play: For toddlers and young preschool children, begin with two leaves cut in half. Place one piece in front of the child and the three other halves in reach. Ask the child to try and find the one that looks the same to make the leaf whole.  For older children provide more choices.

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Continue this game using different types of leaves.  Notice attributes of the leaves and talk/ask questions about the shape. Is it pointy or round, dark green or light green?

4.    Reflect and Assess:  How much assistance did you offer the child? Was the child able to independently choose the correct leaf? Was he able to move and turn the leaf to create a whole? Did you find yourself offering assistance? What other types of puzzles can you create?

What words and language did you and the child use to describe the leaves? Were you surprised by anything?

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Ready: The child is ready if he/she has some experience matching two identical shapes and has taken things apart and put them back together.  It would also be beneficial if the child has explored the property of leaves before being asked to use them for math learning. Observe a small pile of leaves and the attributes before taking them apart.

Play a matching game with similar leaves.

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Extend: Cut larger leaves into four pieces for added challenge.

This game is not just about shape and puzzles. Putting pieces together to create a “whole” introduces the concept of fractions at a basic level.

Below is a picture of my 5 year old’s favorite puzzle game, Pattern Play by Mindware

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Math Games

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As a child I had plenty of time outside. I remember hot summer days playing in the grass and endless sports games staring at the ground, waiting for something to happen. On these occasions one of my favorite things to do was to look for four-leaf clovers. Last week my daughter and I were out hunting when, to our delight, we found one!

Searching for four leaf clovers allowed my daughter a chance to classify plants, notice differences and quickly count leaves.

Today I will share another childhood game that encourages children to use their ever growing brains to predict, count, use one-to-one correspondence and have fun. The game is Rock School.

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How to Use the Blog Posts

PLAYFUL INVITATION

1.    Prepare: Find a set of stairs and a rock.  This game can be played with one or more children.

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.

2.    Invite:  I know this game called Rock School. Would you like to play?

I’ll be the teacher and you’ll be the student. Your job will be to guess which hand I’m hiding a rock.  If you’re right, you get to move to the next “grade” by moving up one step.

3.    Play: Begin with two or more children sitting on the bottom step. Show the children that you have a small rock that fits in the palm of your hand.  Put your hands behind your back and choose a hand to hide the rock.

Looking at the first child, hold out your hands with the rock hidden inside.  Ask: Can you guess which hand has the rock?

Let the child point to a hand, then reveal whether the rock is in the hand or not.  If the child guesses correctly, he/she moves up one step. If not, the child stays on the step and the game continues.… Hide the rock, ask the child to guess, reveal. Then move up or stay in the same place.

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First one to the top wins!

4.    Reflect and Assess: Did the child follow the rules of the game? Did the child use one-to-one correspondence when moving up one, and only one, step? What other counting and number talk did you use as you described where the child was on the staircase? Did you or the child count how many she got right, or how many more steps she needed to win?

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*An added bonus, playing games like this also develops the child’s ability to self-regulate. Children must follow directions, wait for a turn, and maintain focus until the game ends.

Ready: A toddler or young preschool child can play this game even before he/she can fully count with understanding. The game reinforces the child’s budding ability to understand one-to-one correspondence using their full body.

Extend: Switch roles and have the child be the “teacher.” Find larger staircases to play on for a longer game. Have the child write the number on the stairs in chalk.

When playing with a group, gather a bunch of rocks, then let the child keep the rock each time he/she is correct. At the end compare how many each child has and how that relates to who won the game.

**I do not know the origin of the game to give proper credit. My mother taught it to me as a child and she learned it from someone else.

Writing Numbers

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Tornados are a part of life in the midwest. At school we practice tornado drills and at home my children have cuddled in the basement as sirens wailed. Thankfully, a tornado has not touched down near our home. Yet the storms leave their mark. Strong winds break branches off trees and leave puddles sprinkled throughout our neighborhood.  

The casualties of the storm provide loose parts to explore and puddles perfect for play. Once the sun returns, puddles can be used to paint pictures and practice writing numbers.

How to Use the Blog Posts

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PLAYFUL INVITATION

1.    Prepare: You will need a paint brush and a puddle (or water in a pail).

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.

2.    Invite: Did you know you can write with water? If you dip a paintbrush in the water you can paint on the ground.

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3.    Play: Ask Can you write some numbers? Model how the brush can be used to write the number 1 or 2. Watch as the child writes numbers. Encourage the child to write as many numbers as he/she can.  Name each number you see as the child works. Talk about what comes before or after the number he/she created.

*Trace numbers written with chalk.

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*Write some numbers BIG and some numbers small.

*Draw and explore with the materials. If the child draws a picture then count what you see. “You drew one smiley face!”

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4.    Reflect and Assess:  What numbers did the child identify? What numbers did the child write? Are there any numbers that were challenging for the child to identify or write? What else did the child draw or create with the water and brush?

Ready:  The child is ready to start learning numbers as a toddler. Counting 1-10, talking about small quantities, and labeling numbers 1-3 are all important to lay an early sense of number.

Scaffold the child’s learning by writing the numbers first and having the child trace. Then have the child write the numbers independently.

Extend: On hot sunny days count how long the number stays on the sidewalk before it disappears. Match objects with the number to show quantity.



Number Sense

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Playful Invitations is very special in my life. The path I took to start this blog was long, and sometimes hard, but I wasn’t alone. I always had the steadfast voice of my mentor and friend. She taught what I needed to learn, asked thought provoking questions, and always encouraged my efforts. The way she guided my learning is the same process I suggest adults use with children. I realize now that she was modeling a respectful way of teaching that shows confidence and empowers the learner. As I prepare to graduate, I would like to acknowledge Dr. Joy Voss and her incredible influence on the blog and my life.

This Playful Invitation is one of her amazing ideas. 

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Mix, et al. (2012) found that counting and labeling visible sets of objects was more successful in improving preschool children’s number knowledge than only labeling quantities or only counting them. Thus, discussing numbers by counting and labeling objects (e.g., toys in the play area and chairs at the dinner table) seems crucial in supporting young children’s developing numerical knowledge, particularly to help them understand what numbers mean. -Zippert, E. L. ., Diamant-Cohen, B., & Goldsmith, A. Y. . (2017)

How to Use the Blog Posts

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 PLAYFUL INVITATION 

1.    Prepare: Find or draw a hopscotch. Make sure it has numbers in each square. 

If you are in a natural area have the children search to find loose parts. (rocks, leaves, mulch, sticks, plants, flowers, etc.) If there isn’t a source of materials where you play, gather a basket ahead of time.

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Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.  

2.    Invite: Look at this hopscotch! See the numbers in each box? Let’s try and match each number with the same number of things we find outside. 

3.    Play: Begin by asking the child to tell you what they notice about the hopscotch. Listen. 

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Next, talk with the child and identify all of the numbers. 

Then, start with 1. Ask the child to find “1 of something” and place it in the box.

Move on to 2, then 3, 4, 5…

Each time ask the child to match the quantity to the number,

 *A variation would be to toss a stone into a box and have the child gather that number of items. Another is to guide children to search for specific items. “Let’s find 4 green things or Let’s find 5 tiny rocks

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4.    Reflect and Assess: What did the child notice about the hopscotch? (numbers, shapes, size, etc.) Was the child able to match quantity with a number? What strategies did the child use for counting or gathering items? 

Ready: The child is ready for this when he/she can count to ten, identify some numbers 1-10, and has a sense of one-to-one correspondence. 

Extend: Write the number 1 in front of each number to make it more challenging for older preschool or Kindergarten children. Match quantity using physical objects and physical movement. Toss the stone into a box and then hop, stomp, clap, or turn the same number of times. 

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RESOURCES

Kelly S. Mix et al., “Acquisition of the Cardinal Word Principle: The Role of Input,” Early Childhood Research Quarterly 27, no. 2 (2012): 274–83.

Zippert, E. L. ., Diamant-Cohen, B., & Goldsmith, A. Y. . (2017). Math Counts Too! Promoting Family Engagement in Math Activities at Home. Children & Libraries: The Journal of the Association for Library Service to Children15(2), 38–40.

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Collecting Data

Data must be represented in order to be interpreted, and how data are gathered and organized depends on the question. 

-Erikson Institute’s Early Math Collaborative

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The tallest tree on the block can be found in our backyard. This massive Yellow Poplar (aka. Tulip Poplar) is just beginning to show signs of life. Every year the tree goes through noticeable changes as it blooms large yellow and orange flowers in Spring, bright green leaves in Summer and drops scaly cones in Fall. The abundance of gifts from our tree inspires hours of loose parts play.  Each season we are grateful for the beauty the tree brings to our small piece of land.  

By exploring in a way that brings children in contact with different natural materials and seasonal changes, they look more closely at their surroundings and what they have to offer. -Keith, 2018

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 This playful invitation is all about noticing the signs of spring while gathering data. 

 How to Use the Blog Posts

 PLAYFUL INVITATION 

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1.    Prepare: Draw or print a piece of graph paper. Notice your surroundings, and based on what you see decide which colors the child will look for. (rainbow colors, shades of green, etc.) Color one box with each color. Attach the graph paper to a piece of cardboard, an old book or clipboard.

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 Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.

2.    Invite: Talk to the child about Spring and the colors you noticed on trees, flowers, and plants. Ask if they would like to search for colors too.

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3.    Play: Give the child the prepared graph paper and pencil. Encourage the child to document the colors they see. Say: Every time you see a color from your sheet mark the box next to it.  At the end we will see which has the most!  An alternative is for the child to hunt and the adult marks the box. 

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Walk around and observe. Ask open-ended questions about which colors you see many times and which you see less. Near the end of your walk sit down and look at the sheet.  Ask: Which had the most and which had the fewest? Which column is the longest or shortest?

Marking a piece of graph paper with your findings helps the child to begin to see how data can be collected and represented. (i.e. bar graph)

4.    Reflect and Assess: What colors did the child notice? Did the child use vocabulary: a lot, many, less, not as many, big or small?  What other math words did you use. How did the child gather data? Did the child do something different from what you anticipated?

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My first attempt at this activity- the child searched for colors on everything (including signs, cars, trash, etc.) until she filled the entire page.  That’s ok! When children are in control of their learning they are more motivated. I continued to ask questions about how many more we needed and then celebrated when the sheet was full!

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Ready: This activity would be most meaningful for older preschool children with some experience gathering data using physical objects or using pictures to represent data.  

(I also did the activity with a 3yr old and there were benefits derived from merely noticing surroundings, practicing making marks on paper, and talking using math language and vocabulary.)

Extend: Listen to children’s questions about the world and think of ways to support them as they gather data to find answers.  

RESOURCES

Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson Education.

Keith, Lynda. (2017). Developing Young Children's Mathematical Learning Outdoors: Linking Pedagogy and Practice. Routledge

 *The drawing of the Yellow Poplar Tree was from the book: Important Forest Trees of the Eastern United States From: Trees of North America a Golden Field Guide by C. Frank Brookman. Copyright 1968 by Western Publishing Company, Inc.

Geometry

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One day a woman visited my preschool classroom to observe and offer professional development. At snack time she sat with the children and told them a story. This classic tale, The Apple Star Story, is about a boy searching for a little red house with no windows, no door, and a star inside.  As she neared the end of the story she cut the apple in half to reveal the star. The children around the table gasped and pointed excitedly as they realized a star could be found inside an apple.


Thinking back on this memory, I realized the important connection to Geometry. Children need to be taught that 2D shapes lie within 3D shapes. Experiences that involve creating, feeling, and cutting the 3D shape help children develop this understanding.

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 PLAYFUL INVITATION 

1.    Prepare: This playful invitation uses playdough or clay as the material for creating shapes. The recipe I used is listed below. Also, gather an assortment of round shaped items (both flat and solid) and a dull knife or piece of string. 

Observe the child throughout the interaction. Use the Invitation to Play Documentation Toolto collect data. 

2.    Invite: Show me how you make a shape round like a ball. Show children acorns, rocks and other round shapes as inspiration. 

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3.    Play: As the child works talk to him/her about the balls they are rolling and how they are 3 dimensional shapes, called spheres. Ask if they can name other things that are spheres. Have the child roll the playdough on the table or in the palm of their hand. Working with playdough and clay has the added bonus of strengthening muscles in the hand, important for fine motor control. 

Once you have a solid round shape, ask the child to cut it in half. Model how to use a dull knife or piece of string. Open the halves and look at the flat face inside the sphere. Talk about how this shape is a circle (or maybe an oval that you can adjust into a circle). Next, make flat circles. Talk about 2 dimensional shapes.

4.    Reflect and Assess: Did the child notice the difference between the 3D spheres and the 2D circles? What math language are they already using? And what language are they ready to develop? What else did the child create with the play dough?

Ready: The child is ready for this playful invitation when she/he is a toddler. Even if the child can only squish the clay, an adult can model how to create circles and spheres.

Extend: Try making cylinders and talking about the flat faces on each end. These are circles too! Use the clay to form other 2D and 3D shapes.  Children will learn sphere, cone, cylinder, cube, pyramid and rectangular prism in the early years of school. 

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Play dough Recipe:

2 cups all-purpose flour

1 cup salt

2 tbsp cream of tartar

2 cups lukewarm water

2 tbsp of oil (vegetable, corn, canola)

Stovetop pot (I prefer nonstick)

Begin by stirring together the flour, salt and cream of tartar in the pot. Next, add the water and oil. Stir. Cook the mixture over medium heat, stirring constantly. The dough will thickened and form into a ball. Remove from heat and allow to cool. Knead until smooth. Store in a plastic bag or container for a few weeks.

Measurement

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On our drive to Grandma and Grandpa’s house we pass a metropolitan river, which is really part of a sewer and storm water collection system. After a winter of heavy snow, and a few spring rain storms, the water level rises each day.  Today it is unusually full. My children always seem to notice the river and it’s ever changing depth. While driving along this urban oddity we notice the water (or lack of) and talk about it.

These conversations about empty, almost full, and full, remind me how important it is to talk about places in your community and then use those conversations to connect learning experiences back at home and school.  Also, empty and full are beginning concepts related to the child’s developing understanding of measurement.

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PLAYFUL INVITATION

1.    Prepare: Gather recycled containers, food coloring and water. 

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Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data. 

2.    Invite: I wonder if you can fill this BIG container until it is completely full.

3.    Play: Encourage the child to use the small containers to fill one large container. Notice how moving water using the small container takes time and slowly changes the water level in the large container. 

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Talk about depth. Use terms Empty, Full, Half Full, Completely Full, etc. 

Count the number of pours it takes to fill the container. 

Lift the large container and feel the weight. Discuss.

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4.    Reflect and Assess:  What did the child notice about the water? What words did he/she use to describe the water? Did he/she naturally use math language? How did he/she measure attributes while playing?

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Relate this experience to something in the child’s life. Whether it is a local river, a bath tub, or just a drinking cup.  All children have experience with water, and may already know what happens when something becomes too full. 

Ready: Water play is beneficial at any age or stage of development.

Extend: Continue talking about volume and capacity in everyday situations. Find items in the home that are empty and full. 

Finally, read about flooding and learn more about what you can do to conserve water.

MATH LANGUAGE

Attributes- characteristic of an item. Examples include color, shape, texture, size, type, number, etc.

Capacity- the maximum amount something can hold.

Measurement- the process of measuring the size, length, weight, volume and other attributes of an object. 

Volume-The amount of 3-dimensional space something takes up.

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Math Language

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This week I was in a 1st grade classroom observing a lesson about adjectives. The students worked with partners to match small pictures, all the same size, with the corresponding comparison word. They needed to figure out that an apple was big, a pineapple was bigger, and a watermelon was the biggest. While it seemed a simple game, it actually required more critical thinking. The child needed to look at the picture and imagine the size of the object in real life, compare it to the other objects, and then use their understanding of the terms to make a match. The literacy activity required knowledge of math!

This playful invitation encourages adults to find objects, then use direct comparison to label each one as big, bigger and biggest or long, longer and longest. Remember… introducing math vocabulary in authentic situations, using real materials, brings the learning to life. 

How to use the Blog Posts 

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PLAYFUL INVITATION 

1.    Prepare: Gather natural materials that are different sizes. Compare the materials so one is noticeably big, bigger and biggest, or long, longer and longest. I will use a collection of Lotus pods and sticks. 

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data. 

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2.    Invite:  Come see what I have here. Let the child touch and explore the materials before asking him/her to use them for math. Begin by asking, What do you notice about these things?  Listen.

3.    Play: Can you tell me which one is the biggest? Show the child a smaller object and ask, Is it bigger than this one? Continue to compare the objects talking about which is bigger. 

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Then ask the child if he/she can put the objects in order from Big to Bigger to Biggest? 

If the child struggles to order the objects, model, then explicitly point and say, “Look this is big, but this one is bigger, and this one is the biggest!!”

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Make connections to favorite stories, like Goldilocks and the Three Bears, or to family members. You are getting so big, but your brother is bigger, and Daddy is the biggest!

Find ways to do the same playful invitation using length. Talk about how items are Long, Longer and Longest.

4. Reflect and Assess: What did you notice while you played? Did the child determine which was the biggest? longest?  Maybe they labeled one as “small” or “short,” revealing their understanding of comparison and opposites. Was the child able to order the materials without labeling? Was the child able to order the objects and label them big, bigger and biggest? Sometimes children show us what they know even when they don’t have the language to explain.  

Ready: Introducing math words and comparing objects can be beneficial for children of any age (even older infants and toddlers). The child is ready to show their own knowledge of comparison words if he/she compares objects based on their attributes. The child should have heard the terms “big” and “long” in conversations or storybooks.

Ready to move on: The child easily labels the objects Big, Bigger and Biggest or Long, Longer and Longest.

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Extend: Grab an item and ask the child to find another that is bigger or longer. Use an assortment of items to compare (not just similar items that vary in size). For example, instead of using three rocks of varying sizes, use an acorn, a river rock, and a large pinecone. One more idea is to begin talking about ways to use measurement tools to be more precise as you figure out the size of an object. 

MATH LANGUAGE

Critical thinking- the analysis of facts to form a judgement.

Comparison- to look at two or more objects and determine how they are similar or different.

Precision- accurate or exact.

Counting to 10

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Our family has the unique opportunity to be part of a chicken co-op. What makes this so special is that we live in the middle of a major metropolitan city. On a small plot of land, sandwiched between houses and apartments, is a green space turned into an urban garden. Our chicken co-op has exactly ten chickens, so every time we visit we need to count and make sure they are all in the coop. This is challenging because some of the chickens look the same and when people visit they flap and run around excitedly.

Thinking about the challenges I face trying to count ten active chickens, reminds me of the challenges children face when counting to ten. Counting to ten is a major milestone for children, and incredibly important because our counting system is based on tens. In this playful invitation, I encourage you to practice counting to ten using real materials. Also, teach children strategies to organize their counting. 

PLAYFUL INVITATION 

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1.    Prepare: Gather ten or more natural materials. I will use a collection of sand dollars.

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data. 

2.     Invite:  Show me how you count to ten? Begin holding up fingers as the child counts, or as you count together. Practice the counting sequence slowly as you hold up each new finger. After priming the child for counting ask if they would like to count your collection. 

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 3.     Play: Begin by assessing their ability to count ten items. Scatter the materials on the table and ask the child to count them. This will provide information about what the child already knows about counting. Next model how to organize the materials before counting:

a.     Line the objects up in a straight line then explicitly point and count “Did you see how I put these into a straight line before counting? This really helps so I don’t miss any of the things.”

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b.     Bring all the materials into one pile. As you count move each item, one by one, into a second pile. Showing the child how to physically move materials that are counted provides a clear visual of what has been counted and what has not been counted.

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After playing and modeling one or both of these strategies. Ask the child if they can count the same way you counted?  

4.     Reflect and Assess: At the beginning you asked the child to rote count, how did they do? Did they say all the number names in order? As you listened, you held up fingers, supporting their learning that counting has a purpose and can be used to count real objects. When you moved to counting items on the table did they show any beginning counting strategies? After modeling strategies, were they able to use these for their own independent counting? You can determine the child’s cardinality and rational counting skills by asking them “how many did you have all together?” after they count. Children with cardinality will quickly respond “ten.”  Children with developing cardinality may not know the answer or may go back to count the objects again. 

Ready: In order to count to find out “how many” the child needs to know the count sequence in order and must understand that each number counted corresponds with one, and only one, item. This is called Rational Counting.

Ready to move on: The child easily counts a group of up to ten items and then tells how many were counted. Clear strategies (lining up, or making piles and moving items from one to another) are evident.

Extend: Continue counting to ten until the child has a solid understanding. Erikson Institute’s Early Math Collaborative says that “Full rational counting with a strong grasp of cardinality up to 10 is a process that takes usually two to three years to develop. For most children, rational counting starts to show up at the end of preschool or beginning of Kindergarten (p.57).”

Instead of counting ten of the same thing, get creative, count sets of different objects (ten things in the laundry basket, ten things that are mine, ten items found outside) 

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MATH LANGUAGE

Cardinality- understanding that the last number counted represents the quantity of the entire set.

Rote count- the ability to recite the count sequence in the correct order without understanding.

Rational counting- the ability to count in sequence and use one to one correspondence to determine the number in a set. 

RESOURCES

Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson Education.

 Please respect living sea creatures. Do not gather live sand dollars.  See resources like Sanibel Sea School for more information about determining if a sand dollar is living.

https://www.sanibelseaschool.org/experience-blog/2015/11/5/sand-dollars-dead-or-alive

WHAT ELSE CAN YOU COUNT ON A SAND DOLLAR?

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Patterns

“Identifying the rule of a pattern brings predictability and allows one to make generalizations.”

-Erikson Institute’s Early Math Collaborative

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One day an Orb Weaver spider came to live outside our upstairs window. My girls were amazed and quickly named her Spidey. Each day we watched as the web grew larger and larger in a concentric pattern. In the morning, Spidey remained in the corner of the web, safely out of sight.  In the evening, Spidey would reveal herself and rest in the center of the web. For many days, we watched and learned these patterns. Talking about them helped us to predict what we would see. 

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A recent study reported….“Common Core content standards for school math include shape but not patterning knowledge…Since patterning skills in the early years predicted math achievement in fifth grade in this study, the authors suggest that teachers and parents engage young children in activities that help them find, extend, and discuss predictable sequences in objects (patterns).” -Rittle-Johnson, Fyfe, Hofer & Farran, (2017)

In my last post about patterns I focused on the use of colorful fall leaves. For this invitation, I encourage you to use similarly colored materials, therefore, guiding children to identify and use the attributes, size and shape, to explore patterns.

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PLAYFUL INVITATION 

1. Prepare: Gather materials that are similar in color, but vary in size or shape. i.e. different size tree cookies (slices) or leaves. 

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data. 

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2. Invite:  Depending on what the child knows about patterns you may begin with any of these invitations: 

Can you Copy my pattern?

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Complete the pattern. Can you find the missing piece?

Extend my pattern? What comes next?

Create a pattern using these materials?

3. Play: While the child works, talk about the shape and/or the size of the materials. “Oh I see you started with the BIG one, and then two SMALL ones.”

Once a pattern is Copied, Completed, Extended or Created, read the pattern with the child. Ask: Tell me about your pattern? If the child needs support, point and read the pattern with the child. i.e. Big, small, small, Big, small, small. 

4. Reflect and Assess: What attributes did the child notice? Size, shape, color, texture, etc. Which prompt worked best for your child (Copy, Complete, Extend, Create)? How will you continue this game so the child learns that patterns are governed by rules, and that reading the pattern helps to predict what comes next?

Ready: The child identifies patterns in their life and surroundings. 

Ready to move on: The child creates simple patterns on their own with and without a model.

Extend: Encourage the child to continue creating new patterns using the same materials. Practice patterns that grow- use sounds or body (soft, medium, and loud! Soft, medium, loud!). Talk about patterns in your daily life (seasons: Fall, Winter, Spring, Summer). 

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MATH LANGUAGE

Attribute- characteristic of an item. Examples include color, shape, texture, size, type, number, etc.

Pattern- A regularity in the world or created by a person. Patterns repeat in a predictable manner.

RESOURCES

Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson Education.

Clements, D.H., & Sarama, J. (2017)*

Rittle-Johnson, Fyfe, Hofer & Farran, (2017

*full citation can be found on the Research page 

Sets and Sorting

“The same collection can be sorted in different ways.”

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-Erikson Institute’s Early Math Collaborative

Last week I visited a local children’s museum. One area had a small space dedicated to the discovery of rocks. All around were different varieties with light tables, magnifying glasses, microscopes, and scales for weighing. My daughter was particularly taken by the ceiling that contained many different Agate rock slices. As we stared at this beautiful collection, we talked about the many different colors and sizes of Agate. This room offered a perfect example of how one collection of rocks can be sorted in many different ways. 

When children sort they bring structure to a collection of materials. The child puts similar materials together and assigns each group an attribute. Talking with children about sorting helps adults understand the child’s reasoning and provides opportunities to build math vocabulary and concepts. The National Research Council (2009) says, “at all levels of mathematics, one looks for structure,” and experiences identifying structure are precursors to algebraic thinking.

This playful invitation encourages open-ended sorting of colorful flowers, abundant in mid-February when Valentine gifts are starting to wilt. Guide the child to sort in different ways using the same collection.

How to Use the Blog Posts

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PLAYFUL INVITATION

1. Prepare: Gather flowers from old bouquets. Choose sorting containers found around the home or school.

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data. 

2. Invite:  Look at all these colorful flowers! Can you sort the flowers?

3. Play: You may sit back and quietly watch, or you may comment on their sorting. Oh I see you are putting all the pink together and all the yellow together.  

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When the child finishes sorting ask him/her to tell you about the groups.

After talking about the groups, put all the flowers back into the basket and ask them to sort again in a different way.

4. Reflect and Assess: Did the child sort using many different groups? Did the child assign each group a different attribute? Did you provide suggestions? How can you continue sorting in your daily life?

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Ready:The child is ready for sorting if they can match or puts similar items together. The child also can describe why items are sorted into groups.

Ready to move on: This activity is about finding different ways to sort, therefore, this invitation could continue using different collections.

Extend:  Compare the groups that were sorted. Which has more or less. Count how many are in each group. Consider using some form of data representation to show your results. Draw each group or Create using the loose parts.

 MATH LANGUAGE

Attribute- characteristic of an item. Examples include color, shape, texture, size, type, number, etc.

Set- items that are grouped together in a meaningful way.

Sort- organize items based on characteristic/attribute.

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RESOURCES

Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson Education.

Development of Research in Early Math Education (2017)*

Clements, D.H., & Sarama, J. (2017)*

National Research Council (2009)*

*full citation can be found on the Research page 

Counting

“Counting can be used to find out “how many” in a collection.”

-Erikson Institute’s Early Math Collaborative

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One afternoon I sat with a little boy looking at pods we collected from a vine growing on a nearby fence. I asked him to tell me how many there were.

Boy: 1, 2, 3, 4, 5

Me: Are you sure about that? How many are there?

Boy: 1, 2, 3, 4, 5

Me: Okay, so there are how many?

Boy: 1, 2, 3, 4, 5.  

This interaction showed that the boy did not fully understand the purpose of counting. He knew the number names in order, however, he did not know that the last number counted was the quantity of all the items in the group.  

He did not have what is called Cardinality.

“Although adults take it for granted because it is so familiar, the connection between the list of counting numbers and the number of items in a set is deep and subtle. It is a key connection that children must make.” -National Research Council, 2009 p25

Children who recite the number names in order may appear knowledgeable, however, a true understanding of counting occurs when children use counting to find out how many.

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Playful invitation

1. Prepare: Gather about 12 small natural items and a few large leaves. For this activity I will use acorn tops and leaves.

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.

2. Invite: Freddy Frog is looking for a pile of five! Will you help him find the perfect pile with five things?

3. Play: Place a leaf with 1, 2, or 3 items on it in front of the child.

Point to a pile and ask: How many do you think we have in this pile? (*Asking the child to predict provides practice labeling the set with a number at the beginning and allows you to assess their ability to subitize.)  After they say a number- Let’s see if you’re right!

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Model counting: Tap each item with your finger as you count OR count each item and set it to the side (*both strategies help to maintain order so the child does not get confused about which item was already counted)

After counting say: So that group has three! We counted, 1, 2, 3 and there are three in that group.

So how many did we have in that group? (assess their understanding that the last number counted is the amount of the group)

Is this the pile for Freddy Frog?  Remember he wants five.

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Next, point to another pile with a different amount between 1-5. Continue asking how many until you reach the pile of 5.

When the child finds the pile of five celebrate!

4. Reflect and Assess: Did the child predict? If so, they are showing some ability to understand quantity. Were they able to count using one to one correspondence? Did they retell the amount after the items were counted? Did they know whether the pile was right for Freddy Frog?

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*Think about how you can adapt the activity based on the child’s interest.

i.e. “The dinosaur needs to eat exactly 5 leaves. Is this five leaves?” or “The bird needs five sticks to build her perfect nest. Is this five? Let’s count and see.” Continue to vary the number of items. Count together. Decide if it is the right amount or not.

Ready: In order to count to find out “how many” the child needs to know the count sequence in order and must understand that each number counted corresponds with one, and only one, item. This is called Rational Counting.

Ready to move on: The child easily counts a group of up to five items and then tell how many were counted.

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Extend: Count higher numbers of items up to 10 to determine “how many.”

Practice the count sequence to 20. Also, select a number and practice counting on (i.e. Let’s count starting with 6.)

Math language

Cardinality- understanding that the last number counted represents the quantity of the

entire set.

Predicting-   to make an educated guess.

Rote count- the ability to recite the count sequence in the correct order without understanding.

Rational counting: the ability to count in sequence and use one to one correspondence to determine the number in a set.

Subitizing- ability to quickly perceive a number without counting.   

Resources

Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson Education.

National Research Council , 2009, Mathematics learning in Early Childhood*

Clements, D.H., & Sarama, J. (2017)*

Mix, K.S., Sandhofer, C.M., Moore, J.A., & Russell, C. (2012)*

*full citation can be found on the Research Page

Spatial Sense

“Relationships between objects and places can be described with mathematical precision.”

-Erikson Institute’s Early Math Collaborative

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In a kindergarten class, a group of four children were excitedly planning to act out the story The Three Billy Goats Gruff.  I sat nearby and watched as the children marked out space for the stage, then dragged props from around the room. For 15 minutes I watched as the children negotiated the perfect placement for the bench (the bridge), a blue princess dress (the creek), chairs (hillside), and finally, a spot for all the characters to stand. Without any adult interaction, the children negotiated using language, “on top of, under, over there, next to, up, down” and many more.  After organizing every last detail, it occurred to me that without experience with these spatial terms the play would not have been a success.

“Children explore spatial concepts through play from an early age. For instance, building with blocks and playing with puzzles have both been linked to stronger spatial skills. Additionally, young children who hear more spatial words from their parents tend to talk about space more themselves, and these same children perform better on later spatial reasoning tasks.”

-Eason & Levine, 2017

The language we use to describe an object’s position in space helps children to learn and understand spatial relationships. This activity provides an opportunity to use this rich spatial language.

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Playful Invitation

1. Prepare: For this activity gather an assortment of natural materials and paper/writing tools or a camera (like many people have on their phone). 

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Arrange the materials in any way. Be sure some items are placed in what could be described as, “next to, on top of, under, above, below, in front of or behind.” Once materials are arranged, snap a photo or draw a quick sketch.

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.

2. Invite: Show the child the drawing/photo and ask if he/she would like to try and recreate the picture.

3. Play: Work alongside the child, observing as he/she positions objects to recreate the picture. If necessary, guide the child using spatial relationship language (next to, on top of, under, above, below, in front of and behind).

Ask open-ended questions: How did you know to put that one there? OR Where does this belong?

Model thinking: Talk out loud as you place an item. I see the leaf belongs under the lily pod, so I’ll put it down first and then I’ll put the lily pod on top of the leaf!

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4. Reflect and Assess: Did the child show an understanding of spatial relationships? Which position words did they know and which did they struggle with?  Did the child follow directions when asked to place an object in a certain position? Did the child use spatial relationship words on their own to describe their thinking?

Ready: The child understands position words (in, on, under, up, down) and follows directions related to proximity (next to, above, beside).

Ready to move on: The child recreates the arrangement with the assistance of an adult, describing the position of objects using spatial terms.

Extend: Lessen the assistance you provide and encourage the child to recreate on their own. When the child finishes ask him to use spatial language to describe where he placed the items OR while the child works have her talk about where she places objects and why.

Challenge the child to create another arrangement that you will recreate.

Math language:

Precision- exact and accurate

Relationships- the state of being connected

Spatial Positions- an objects position in space in relation to other object/s (up, down, above, below, next to, under, etc.)

Spatial Relationships-  how an object is located in space in relation to another object.

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Resources:

Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson Education.

Clements, D.H., & Sarama, J. (2017)*

Eason, S.H., & Levine, S.C. (2017)*

National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence.*

*full citations can be found on the Research page

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Counting Large Numbers

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Lately my child is obsessed with counting to 100. At school, the class is gearing up for the “100th day of school” and teachers are asking the children to try and count as high as they can. A simple counting book from the library with a page that shows 100 baby chicks is a favorite. Right before bed she pulls out the book and insists on counting all 100 chicks. I am both proud and impatient as I stare longingly at the clock and hope she counts fast.  

“Providing opportunities for children to count collections greater than 20 (even as they may still be struggling with the teens) can help them to engage with its underlying structure. In attempting to count further, children’s emerging understanding of the base-ten number system is often revealed.” 

–Carpenter, Franke, Johnson, Turrou and Wager (2017)

Children are not expected to count large numbers before entering Kindergarten, however, some preschool children are ready and excited to explore higher numbers. Some children may enjoy counting collections and feel proud as they count higher and higher. Often, listening as children count higher numbers reveals what they know, and do not know, about our number system. For instance, a child who counts 1-29 and then says twenty ten, twenty eleven… reveals an opportunity to talk about decades, and how the count sequence changes after a 9. (i.e. 9-10, 19-20, 29-30 and beyond). Watching children count physical objects also reveals counting strategies including organizing or grouping a large collection before counting. 

PLAYFUL INVITATION

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1.     Prepare: Gather 100 or more objects from nature. Also, consider creating a 100 grid using chalk on the sidewalk or a piece of poster board.

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Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data. 

2.     Invite: Will you help me count this collection of things? I want to see if I have 100!

3.     Play:  Ask open-ended questions: What should we do first? 

Observe, does the child immediately begin counting, organize/sort the group, or place items on each square of the grid?  There is no right or wrong way. This is all about seeing what children know. At first, simply provide the materials and be a “watcher.”

Consider asking guiding questions: Is there a way we can get organized so we don’t count the same things more than once? This grid has one-hundred squares, maybe we could use this to help us count? OR Look each row has ten boxes. Every time we start a row we say something a little bit different!  OR Let’s count together (practice the count sequence and deliberately stress 10, 20, 30, 40…etc.)

Continue observing, offer guidance when necessary, and ask open-ended questions. 

 4.    Reflect and Assess: While counting, did the child skip any numbers, forget their place, or make any errors? What numbers were challenging to the child? What strategies does the child use to keep track of what he/she already counted? Does he/she line the items up, organize them in some way, or even put them into groups of 10?

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Ready: The child can accurately count large numbers of items (10-20) using one to one correspondence and the child knows the count sequence beyond 20.

Ready to move on: If the child easily counts a collection of 100 items.

Extend: Count higher numbers beyond 100. Introduce counting by twos, fives, or tens. Count on from a number. Say let’s start at 29, what comes next?

MATH LANGUAGE

Base Ten Number System- The base-ten number system consists of ten digits (0,1,2,3,4,5,6,7,8,9) and groups number into tens.

One to One Correspondence- When counting a set, each item should be counted only once matching one number word to each item.

RESOURCES 

Clements, D.H., & Sarama, J. (2017)*

Carpenter, T.P., Franke, M.L., Johnson, N.C., Turrou, A.C., and Wager, A.A. (2017). Young children’s mathematics: Cognitively guided instruction in early childhood education. Portsmouth, NH: Heinemann.

*full citation can be found on the Research Page

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Counting

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“Counting has rules that apply to any collection”

-Erikson Institute’s Early Math Collaborative

Like most parents and teachers we make up rules. Some typical: Do not throw toys inside.  Some unusual: Do not eat the dog food! Whatever the reason, rules serve a purpose.

In preschool math, there are also rules. Counting, for example, has four rules. And, incredibly, most children learn the rules of counting without ever hearing them stated.

The Rules of Counting:

  1. Number words are said in the same order every time. (stable order)

  2. Each item should be counted only once, matching one number word to each item.

    (one to one correspondence)

  3. A set of items can be counted in any order and the result will be the same.

    (order irrelevance)

  4. The last number counted is the quantity of the set. (cardinality)

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How to use the Blog Posts

Playful Invitation

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1. Prepare: Cut an egg carton so it has ten cups. (Working with ten is important because our number system is based on a system of tens) Provide an assortment of small natural loose parts, or ask the child to walk around outside to gather items on their own.

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.

2. Invite: Hand the child the container and say: Here is a container that I want you to fill with a few special things you find. Put only one item in each cup. Off you go!

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3. Play: When the child returns, say: Let’s look at what you found! Notice whether the child used one to one correspondence and placed only one item in each cup.  If not, then work with the child to move or remove items so there is only one item in each cup. Modeling and practicing one to one correspondence will support the child’s ability to count.

Once items are in the cups ask How many did you gather?  Explicitly point to each item as the child or adult counts using the stable order principle.

Ask: So how many was that? to assess their understanding of cardinality. Hold up the same number of fingers to symbolize the number of items in their container.

Using the same collection, or another collection gathered by a peer, count again.  This time count from the bottom row of the container or spin the container and count vertically. This shows the child that the order is irrelevant and the collection could be counted in many different ways.

4. Reflect and Assess: Make a list of the four counting rules.  Place a check next to each one as you work with the child. What do you notice about the child’s ability to count?

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Ready: The child is ready for this activity if he/she can count to 10 with understanding (most of the time), and can label small quantities of items.  If the child struggles then try the activity using only three - five cups. Also, continue counting 1-10 using songs, counting body movements (stomps or jumps) and counting items.

Ready to move on: If the child easily counts to 10, can gather 1-10 items when asked, uses one to one correspondence when counting, and determines the quantity in their container.  

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Extend: Specify the number of items the child should find. (Can you find five items?)

Increase rote counting to 20.  

Use two containers for gathering items and then add them together.  Write the final number on the ground with chalk.

This activity also supports the development of concepts like full, half full and empty (precursors to fractions) and spatial relationships like on and in.

According to the National Research Council- For now focus on whole items rather than looking at features of an item. For instance, points on a leaf, leaves on a tree branch, or branches on a tree, may seem like good ideas for counting, however children need time and practice before they learn to count parts of a thing. For now just count the “thing” as a whole. NRC, 2009, 136

Math language:

Cardinality- understanding that the last number counted represents the quantity of the entire set.

One to one correspondence- when counting a set, each item should be counted only once matching one number word to each item.

Order Irrelevance- items can be counted in any order and the result will be the same.

Rote count- the ability to recite the count sequence in the correct order without understanding.

Stable order- number words are said in the same order every time

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Resources:

Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson Education.

National Research Council (2009)*

*full citation can be found on the Research Page

Subitizing

“The quantity of a small collection can be intuitively perceived without counting.”

-Erikson institute’s Early Math Collaborative

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When my daughter and I started playing games with dice I noticed her ability to quickly call out the number without actually counting the dots.  She rolled three dots, and without counting, said THREE! How did she learn to do that?

Later, I attended a conference session all about Subitizing- the ability to quickly perceive a number without counting.  Subitizing is very important in early childhood and something we all use in our day to day life.

The primary focus in most preschools is to teach children to count, however research has shown that another crucial skill is attaching number words “labels” (one, two, three) to small sets of objects. This is an essential stepping stone to developing an understanding of quantity.

-Nguyen, Laski, Thomson, Bronson, & Casey, 2017

In this playful invitation focus on developing the ability to label small groups without counting. Preschoolers begin to use subitizing with 1, 2 and 3 items.  As they grow in their abilities they see 4, 5, and 6. You can practice your child’s ability to quickly perceive an amount by playing simple games.

How to use the Blog Posts

Playful Invitation

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1. Prepare: 5 shells, acorns, or other natural material, and a piece of paper, cardboard, or fabric. Sit facing the child with the materials on the table/ground and the paper/fabric/cardboard hiding the materials from the child’s view.

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.

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2. Invite: I have a game to play with you! When I move this paper you will see some shells/rocks/etc.. I want you to take a quick peek and tell me how many you saw.

3. Play:

Secretly place two shells on the table or ground and cover with the paper. Quickly reveal the item for about 3 seconds and then cover again.

Ask: How many did you see? and How do you know?

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Model thinking and counting: Wow, so you knew the number without even counting? You’re right! There were two. See, 1, 2! Deliberately point and count.

Vary the amount (no more than 5 to start) to challenge the child.

4. Reflect and Assess: How did the child do with this game? Was the child able to instantly name the amount without counting? What number of items posed a challenge?

Ready: The child is ready if he/she shows an understanding of one, two and more. Also the child knows the number words one, two, three and beyond.

Ready to move on: The child quickly calls out the number when shown 1, 2, 3 items.

Extend: Work on subitizing to 5.

Also, try combinations of materials or colors. For example, two rocks and two shells. Ask How many did you see? Then ask How many were rocks? and How many were shells?

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Noticing smaller groupings within the set is the beginning of Conceptual Subitizing- when you quickly perceive smaller groups within the set and use these to determine the amount. Check out this video at mathisvisual.com for a fun example based on the ideas of Jo Boaler.

Another idea I play with my children is “Fingers, Fingers,” developed by Kristen Reed and Jessica Mercer Young. Check out their great article about games: https://www.naeyc.org/resources/pubs/tyc/oct2017/play-games-learn-math-explore-numbers; Youtube video

*One additional thought. It is recommended that children primarily practice Subitizing with simple dots. Consider how you can incorporate dice and dot cards into your daily routines and math games.

MATH LANGUAGE

Quantity- the amount of something. The “how many or how much.”

Perceived- to understand or realize something.

Subitizing- ability to quickly perceive a number without counting.   

Conceptual Subitizing- when you quickly perceive smaller groups within the set and use these to determine the amount.

Set- items that are grouped together in a meaningful way.

Number sense- the ability to understand the quantity of a set and the name associated

with that quantity.

Resources

Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson Education.

Clements, D.H., & Sarama, J. (2017)*

Reed, K., & Young, J.M. (2017)*

Nguyen, Laski, Thomson, Bronson, & Casey, 2017*

Mathisvisual.com

* full citations can be found on the Research Page

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Collecting Data

“The purpose of collecting data is to answer questions when the answers are not immediately obvious.”

-Erikson Institute’s Early Math Collaborative

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This past week I had the opportunity to walk along the beach with my preschool-aged children and marvel at the abundance of seashells. My older child is very interested in big numbers and often combines numbers she’s heard into unusual and enormous combinations. She asked if I knew how many shells were on the beach. “I don’t know?” I replied. Excitedly she said…“I think there are thirty two hundred thousand and sixty thousand!”  This made me wonder, could she be right?

“The collection of data should ideally start with a question of interest to children.” –NRC 2009 

This playful invitation is a basic start to data collection, asking and answering questions that involve math. The idea for the blog was inspired by my child’s spontaneous questions as we looked at shells on the beach. “I wonder which one has the most?” she asked. 

While each child’s questions about the world are different, one way to encourage interest in data collection is to pose a question yourself and work together to figure out the answer.  

PLAYFUL INVITATION

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1.     Prepare: Gather a large collection of natural loose parts. Think about having multiple items that are the same within the collection. Ideas might include: various colored fall leaves, different materials that fall from trees, shells, etc.

Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data. 

2.     Invite: Display the materials in a random order. Say, Let me show you something….I have this big  collection of shells and I’m wondering which type of shell has the most. I really want to figure it out. Will you help me answer my question? 

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3.     Play:  Ask the child What do you think I should do first? Follow the child’s lead and really listen to their reasoning. 

If he/she seems stuck scaffold through questions and suggestions. i.e. Perhaps we could sort all the shells? OR I see a lot that look like this (point to one type) first let’s find all of this kind.

Once the shells are in groups ask the child, What do you notice about these groups? Which one has the most? How do you know?

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Using a piece of paper, or a stick in the sand, write numbers/tally marks/dots.  Talk about your findings. Which had the most/least/same. Why is collecting data useful?

4.     Reflect and Assess: What did you learn about the child’s strategies for problem solving? Was the child able to develop a plan to answer the question?  Did his/her suggestions lead you down a different path than you thought? Did you see the child using skills like sorting, classifying, counting, estimating, measuring, etc. 

What other questions about the world do children ask?  Pay attention. Take advantage of the authentic opportunities for math learning that stem from their inquiry.

Ready: The child is ready for this activity if he/she can count with understanding, knows ordinal numbers (1st, 2nd and 3rd) and has basic sorting skills.

Ready to move on: If the child uses problem solving skills to gather relevant data, and determines the answer to simple math questions involving small numbers, then he/she is ready to extend.

Extend: Represent findings using simple graphs. Gather data in other ways, for example, simple surveys of peers. Use larger numbers when exploring data.

MATH LANGUAGE

Sort- organize items based on characteristic/attribute.

Reasoning- thinking about something in a logical way. Children are asked to explain their answers so an adult and/or other children can hear the thought process or reasoning that went into solving a problem.

Problem Solving- finding a solution to a question, issue, or problem. 

Ordinal Number- tells the position of an object when it is part of a list. 1st, 2nd, 3rd, 4th, etc.

RESOURCES 

Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson Education.

National Research Council , 2009, Mathematics learning in Early Childhood*

Clements, D.H., & Sarama, J. (2017)*

*full citation can be found on the Research Page

 HAPPY NEW YEAR!

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